University of KashanIranian Journal of Mathematical Chemistry2228-64892008-90158320170901Autobiographical notes231257ENN.Trinajstićtrina@irb.hr10.22052/ijmc.2017.64354.1248I was born in Zagreb (Croatia) on October 26, 1936. My parents were Regina (née Pavić) (April17, 1916, Zagreb–March 9, 1992, Zagreb) and Cvjetko Trinajstić (September 9, 1913, Volosko–October 29, 1998, Richmond, Australia).Chemical graph theory,mathematical chemistry,Nanad Trinajstichttp://ijmc.kashanu.ac.ir/article_45087.htmlhttp://ijmc.kashanu.ac.ir/article_45087_dcb8952d03d7c0cf9d02f509573121d2.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90158320170901Graphs with smallest forgotten index259273ENI.GutmanUniversity of Kragujevac, Serbiagutman@kg.ac.rsA.GhalavandUniversity of Kashanali797ghalavand@gmail.comT.Dehghan-ZadehUniversity of Kashanta.dehghanzadeh@gmail.comA.R.AshrafiUniversity of Kashanijmc@kashanu.ac.ir10.22052/ijmc.2017.43258The forgotten topological index of a molecular graph $G$ is defined as $F(G)=sum_{vin V(G)}d^{3}(v)$, where $d(u)$ denotes the degree of vertex $u$ in $G$. The first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number $gamma=1,2$, the first through the fourth for $gamma=3$, and the first and the second for $gamma=4,5$ are determined. These results are compared with those obtained for the first Zagreb index.Forgotten topological index,Unicyclic graphs,Bicyclic graphs,Tricyclic graphs,Tetracyclic graphs,Pentacyclic graphshttp://ijmc.kashanu.ac.ir/article_43258.htmlhttp://ijmc.kashanu.ac.ir/article_43258_0b9303cff3a4e0713b73cf33798147fb.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90158320170901On the first variable Zagreb index275283ENK.MoradianDepartment of Statistics, Islamic Azad Universityrst.kazemi@gmail.comR.KazemiImam Khomeini international universityr.kazemi@sci.ikiu.ac.irM.H.BehzadiDepartment of Statistics, Islamic Azad Universitybehzadi.mh@gmail.com10.22052/ijmc.2017.71544.1262‎The first variable Zagreb index of graph $G$ is defined as‎ ‎begin{eqnarray*}‎ ‎M_{1,lambda}(G)=sum_{vin V(G)}d(v)^{2lambda}‎, ‎end{eqnarray*}‎ ‎where $lambda$ is a real number and $d(v)$ is the degree of‎ ‎vertex $v$‎. ‎In this paper‎, ‎some upper and lower bounds for the distribution function and expected value of this index in random increasing trees (recursive trees‎, ‎plane-oriented recursive trees and binary increasing trees) are‎ ‎given‎.First variable Zagreb index‎,‎Random increasing‎ ‎trees‎,‎Distribution function‎,‎Expected valuehttp://ijmc.kashanu.ac.ir/article_45113.htmlhttp://ijmc.kashanu.ac.ir/article_45113_2a098655d1e3c140f89c3276a97f9e78.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90158320170901Computing the additive degree-Kirchhoff index with the Laplacian matrix285290ENJ.PalaciosThe University of New Mexico, Albuquerque, NM 87131, USAjpalacios@unm.edu10.22052/ijmc.2017.64656.1249For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.Degree-Kirchhoff index,Laplacian matrixhttp://ijmc.kashanu.ac.ir/article_48532.htmlhttp://ijmc.kashanu.ac.ir/article_48532_3d7984d6e1bc469b6c8dc075c7bf9610.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90158320170901On the spectra of reduced distance matrix of the generalized Bethe trees291298ENA.HeydariArak University of Technologya-heidari@iau-arak.ac.ir10.22052/ijmc.2017.30051.1116Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.Reduced distance matrix,Generalized Bethe Tree,spectrumhttp://ijmc.kashanu.ac.ir/article_48533.htmlhttp://ijmc.kashanu.ac.ir/article_48533_93ac14d2ea7c08d919a6c30039ff1ded.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90158320170901On the second order first zagreb index299311ENBBasavanagoudKARNATAK UNIVERSITY DHARWADb.basavanagoud@gmail.comS.PatilKarnatak Universityshreekantpatil949@gmail.comH. Y.Denghydeng@hunnu.edu.cn10.22052/ijmc.2017.83138.1284Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zagreb index, is better than models corresponding to the first Zagreb index and F-index. Further, we compute the second order first Zagreb index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p; q], tadpole graphs, wheel graphs and ladder graphs.Topological index,line graph,subdivision graph,Nanostructure,tadpole graphhttp://ijmc.kashanu.ac.ir/article_49784.htmlhttp://ijmc.kashanu.ac.ir/article_49784_8a12c9b7c5c6942e17923e06c1f223ee.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90158320170901Anti-forcing number of some specific graphs313325ENS.AlikhaniYazd University, Yazd, Iranalikhani@yazd.ac.irN.SoltaniYazd Universityneda_soltani@ymail.com10.22052/ijmc.2017.60978.1235Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by $af(G)$. In this paper we consider some specific graphs that are of importance in chemistry and study their anti-forcing numbers.Anti-forcing number,Anti-forcing set,Corona producthttp://ijmc.kashanu.ac.ir/article_49785.htmlhttp://ijmc.kashanu.ac.ir/article_49785_63810586ce414d4cc8a97c6dbf37dcb3.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90158320170901On the forgotten topological index327338ENA.KhaksariDepartment of Mathematics, Payame Noor University, Tehran, 19395 &ndash; 3697, I. R. Irankhm.paper@gmail.comM.GhorbaniDepartment of mathematics, Shahid Rajaee Teacher Training Universitymghorbani@srttu.edu10.22052/ijmc.2017.43481The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.Zagreb indices,Forgotten index,Graph productshttp://ijmc.kashanu.ac.ir/article_43481.htmlhttp://ijmc.kashanu.ac.ir/article_43481_12fee5261e77f9121b93d736c6102d79.pdf